Static Distortions in Liquid Crystals

Yd axis, respectively. The six components of curvature strain at this point are defined by (Fig. 6.3) 

The splay (Kn) deformation is described by a and and gives a non-zero V twist K22) deformation is described by 02 and 04 and gives 

Frank wrote down the Gibbs free energy density (/) of deformation relative to its value in a state of uniform orientation [6.29] as 

FIGURE 6.3. Three types of deformation in a director field (a) splay gives 7. n(f) 0, (b) twist gives h f) V 7 0, and (c) bend gives 

In a smectic A phase, deformations that do not preserve interlayer spacing of the layered structure would cost a great amount of energy. For a dislocation-free sample, it can be shown that y x n = 0. Thus, both twist and bend deformations are absent. In other words, U2 — U4 = 0 and asi + aej = 0. Under these conditions, the Ks in / [Eq. (6.12)] obey the fact that K22 and Kss are much larger than the others. Values of K22 and 

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